Exam 20: The Second Law of Thermodynamics

Energy in capacitors: The capacitive network shown in the figure is assembled with initially uncharged capacitors. A potential difference, V_ab = +100V, is applied across the network. The switch S in the network is kept open. Assume that all the capacitances shown are accurate to two significant figures. What is the total energy stored in the seven capacitors?

Dielectrics: A 15-μF air-filled capacitor is connected to a 50-V voltage source and becomes fully charged. The voltage source is then removed and a slab of dielectric that completely fills the space between the plates is inserted. The dielectric has a dielectric constant of 5.0. (a) What is the capacitance of the capacitor after the slab has been inserted? (b) What is the potential difference across the plates of the capacitor after the slab has been inserted?

Capacitors in combination: Three capacitors, with capacitances = 4.0 μF, = 3.0 μF, and = 2.0 μF, are connected to a 12 -V voltage source, as shown in the figure. What is the charge on capacitor ?

Dielectrics: A 6.0-μF air-filled capacitor is connected across a 100-V voltage source. After the source fully charges the capacitor, the capacitor is immersed in transformer oil (of dielectric constant 4.5). How much ADDITIONAL charge flows from the voltage source, which remained connected during the process?

Energy density: Each plate of an air-filled parallel-plate air capacitor has an area of 0.0040 m², and the separation of the plates is 0.080 mm. An electric field of 5.3 × 10⁶ V/m is present between the plates. What is the energy density between the plates? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Cylindrical capacitors: An air-filled capacitor is formed from two long conducting cylindrical shells that are coaxial and have radii of and The electric potential of the inner conductor with respect to the outer conductor is (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²) The energy stored in a 1.0-m length of this capacitor is closest to

Cylindrical capacitors: The capacitance per unit length of a very long coaxial cable, made of two concentric cylinders, is 50 pF/m. What is the radius of the outer cylinder if the radius of the inner one is 1.0 mm? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Dielectrics: A parallel-plate capacitor, with air between the plates, is connected across a voltage source. This source establishes a potential difference between the plates by placing charge of magnitude on each plate. The space between the plates is then filled with a dielectric material, with a dielectric constant of 7.74. What must the magnitude of the charge on each capacitor plate now be, to produce the same potential difference between the plates as before?

Capacitors in combination: The network shown in the figure is assembled with uncharged capacitors X, Y, and Z, with , and and open switches, S₁ and S₂. A potential difference V_ab = +120 V is applied between points a and b. After the network is assembled, switch S₁ is closed for a long time, but switch S₂ is kept open. Then switch S₁ is opened and switch S₂ is closed. What is the final voltage across capacitor X?

Parallel-plate capacitors: The electric field between square the plates of a parallel-plate capacitor has magnitude E. The potential across the plates is maintained with constant voltage by a battery as they are pulled apart to twice their original separation, which is small compared to the dimensions of the plates. The magnitude of the electric field between the plates is now equal to

Cylindrical capacitors: An air-filled capacitor is formed from two long conducting cylindrical shells that are coaxial and have radii of and The electric potential of the inner conductor with respect to the outer conductor is (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²) The maximum energy density of the capacitor is closest to

Dielectrics: A charged capacitor stores energy U. Without connecting this capacitor to anything, dielectric having dielectric constant K is now inserted between the plates of the capacitor, completely filling the space between them. How much energy does the capacitor now store?